Note that, for graphs, one can give an alternative definition of the tree-width a graph \(G\)  as: \(\operatorname{\mathbf {tw}}(G) = \min \lbrace \omega (H) -1 : H \text{ chordal completion of } G\rbrace \)  (where \(\omega \)  is the clique number) [1]}. With this in mind, observe that the following definition of the width of a pseudo-chordal completion furthers the analogy between our construction and the tree-width of graphs.
